Unfortunately, the issues you are experiencing are symptomatic of an internal hardware defect, often a faulty power supply or main/control board, though there are many possible failure points. This issue could be a manufacturing defect, but is also often caused by a power event (shock/surge, prolonged over/under voltage condition, etc). Since you have no signs of life from it at all, you almost certainly have a fried power supply board, at a minimum.This could also be the result of age related wear and tear, as a 2011 model tv, that type of failure wouldn’t be surprising. There is one step you can take here, both as a possible fix, as well as a diagnostic evaluation1) Unplug the power cord from the tv2) Wait at least 1 hour (60+ Minutes)3) Press and hold the power button (on the set, not the remote) for 60 seconds4) Keep holding power button while plugging back in, and for another 60 seconds after. When plugging back in, go directly to the wall outlet, bypassing any power strips or surge protectors. If this reset process does not work, it would unfortunately confirm an internal hardware failure. This is something that would require repairs to correct; if you're thinking about a do it yourself repair, you'll need to be comfortable and skilled with electronics repairs, which would require dismantling the set (removing the back panel of the tv), diagnostics with a digital multimeter to test voltages inside, changing out boards as needed, and possibly desoldering/removing and soldering/replacing capacitors (a common failure point).If you’re considering repair at a local shop, you’ll find a typical repair to be around $300 for diagnostics, parts, and labor. For a tv of this size, replacement often makes more sense though, especially in cases of surge damage where multiple parts may be damaged, which drives the parts cost up significantly. You can get a brand new LED tv
with a fresh warranty in the $500 range. Depending how you’d like to proceed here, I can help with finding parts, finding a repair shop, or recommending replacement options. Just let me know.